# 6.soru - 1 You are given a ticket for running a red traffic...

This preview shows pages 1–3. Sign up to view the full content.

1) You are given a ticket for running a red traffic light. For an observer halted at the red light, the light emits a wavelength λ 0 = 700 nm. You tell the traffic cop that because you were approaching the light, the Doppler shift made it appear green ( λ = 500 nm). How fast would you have been going if this smart-aleck explanation had been true? Please express this speed in units of miles per hour. [Hint: There are 1.6093 kilometers in a mile.] First, Δ λ = λ - λ 0 = 500 nm - 700 nm = - 200 nm . In words, the wavelength decreased by 200 nm, making it appear green (we would call this a blueshift). Δ λ < 0 implies that we’re moving toward the traffic light (as expected). This is a useful consistency check. By convention, if the relative velocity of two objects is negative (i.e., v < 0), then they are getting closer together. This is because the distance that separates them is decreasing as time goes on. Next we determine the driver’s velocity ( v ). The wavelength change is related to velocity by the following formula: Δ λ λ 0 = v c , where Δ λ is the change in wavelength, λ 0 is the wavelength at rest (in the lab), c is the speed of light, and v is radial velocity (along the line of sight). Multiplying both sides of the equation by c , we find: v = c Δ λ λ 0 . Plugging in the numbers from above and c = 3 . 0 × 10 5 km/s, we have: v = (3 . 0 × 10 5 km/s) parenleftbigg - 200 nm 700 nm parenrightbigg = (3 . 0 × 10 5 km/s) × parenleftbigg - 2 7 parenrightbigg = - 8 . 571 × 10 4 km/s Note that the units of wavelength (nm) canceled out. Lastly, we must convert km/s to miles per hour ( mph). The hint indicates that 1 mi = 1 . 6093 km and we know that 1 hr = 3600 s (1 hr = 60 min × 60 s / min = 3600 s). Combining these two we get: 1 km/s = 1 km/s × parenleftbigg 1 mi 1 . 6093 km parenrightbigg × parenleftbigg 3600 s 1hr parenrightbigg 2237 mph Putting all this together we find: v = ( - 8 . 571 × 10 4 km/s ) × parenleftbigg 2237 mph 1 km/s parenrightbigg ≈ - 1 . 92 × 10 8 mph 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2) Astronomers doing a ”star census” of the solar neighborhood have found that there are 340 stars within a distance r = 10 pc of the Earth. Compute the volume of a sphere of radius r = 10 pc centered on the Earth. Compute the average number of stars per cubic parsec within this sphere.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern